Solve for x x^4-4x^3-x^2+4x=0

Problem

x4−4*x3−x2+4*x=0

Solution

1. Factor out the greatest common factor, which is x from all terms in the equation.

x*(x3−4*x2−x+4)=0

2. Group terms inside the parentheses to perform factoring by grouping.

x*((x3−4*x2)+(−x+4))=0

3. Factor out common terms from each group: x2 from the first group and −1 from the second group.

x*(x2*(x−4)−1*(x−4))=0

4. Factor out the common binomial (x−4)

x*(x−4)*(x2−1)=0

5. Apply the difference of squares formula to factor x2−1

x*(x−4)*(x−1)*(x+1)=0

6. Set each factor to zero using the zero product property to find the values of x

x=0

x−4=0⇒x=4

x−1=0⇒x=1

x+1=0⇒x=−1

Final Answer

x={−1,0,1,4}

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